{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 06\n",
    "\n",
    "# 三维参数方程\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0365e62-cf7e-42bb-a04e-5627924db9fe",
   "metadata": {},
   "source": [
    "这段代码的核心任务是生成并可视化一条三维螺旋线，同时对图形的外观和视角进行调整，最终展示一条从原点开始，沿着空间逐渐上升的三维曲线。\n",
    "\n",
    "### 数学背景\n",
    "代码首先定义了参数变量 $t$，它是一个从 $0$ 到 $8\\pi$ 均匀分布的数值数组，包含 $200$ 个点。参数 $t$ 作为自变量用于生成三维空间中的螺旋线，其对应的参数方程为：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x_1 &= \\cos(t), \\\\\n",
    "x_2 &= \\sin(t), \\\\\n",
    "x_3 &= t.\n",
    "\\end{aligned}\n",
    "$$\n",
    "这组方程描述了一条参数曲线，其中 $x_1$ 和 $x_2$ 描述了水平面上的圆周运动，而 $x_3$ 描述了曲线在 $z$ 轴方向的线性上升。因此，这是一条围绕 $z$ 轴旋转并不断向上的螺旋线。\n",
    "\n",
    "### 图形创建与参数调整\n",
    "代码使用 Matplotlib 库绘制该曲线，并对图形进行了以下操作：\n",
    "1. **三维绘图环境**：通过 `plt.figure()` 创建图形对象，并用 `plt.axes(projection='3d')` 设置三维坐标轴。\n",
    "2. **绘制曲线**：使用 `ax.plot(x1, x2, x3)` 依次传入 $x_1, x_2, x_3$，绘制螺旋线。\n",
    "3. **投影设置**：采用正交投影 (`ortho`)，以保持图形各部分比例一致。\n",
    "4. **坐标轴范围**：为确保图形居中，分别设置 $x, y$ 轴范围为 $[-1.5, 1.5]$，并将 $z$ 轴范围设定为 $[0, t_{\\text{max}}]$，即 $z$ 的最大值为 $8\\pi$。\n",
    "5. **视角调整**：通过 `ax.view_init` 将视角设置为方位角 $-135^\\circ$ 和仰角 $30^\\circ$，提供一个更直观的观察角度。\n",
    "6. **网格样式**：将各坐标轴网格线的线宽调整为 $0.25$，并采用点线样式，使图形更加清晰。\n",
    "\n",
    "### 坐标轴标签与布局\n",
    "每个坐标轴分别被标记为 $x_1, x_2, x_3$，对应于螺旋线的三个维度。此外，使用 `plt.tight_layout()` 自动调整图形的布局，避免标签重叠。\n",
    "\n",
    "### 可视化效果\n",
    "通过这些操作，生成的三维螺旋线清晰地展示了以下特性：\n",
    "1. **圆周运动**：在水平面上，螺旋线沿单位圆路径旋转。\n",
    "2. **线性上升**：在 $z$ 轴方向上，螺旋线随着 $t$ 的增大而均匀上升。\n",
    "3. **整体结构**：曲线呈现规律性与美观性，可用于研究三维几何形态或生成艺术化图形。\n",
    "\n",
    "总结来说，这段代码不仅实现了三维空间中参数曲线的绘制，还提供了详细的图形调整功能，使得绘图效果符合科学研究或视觉展示的需求。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7909d117-c075-4497-a179-ff1bd54c90cc",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f09ef896-08f2-41ac-af4f-695aab3d012f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入numpy库，用于数值计算\n",
    "import matplotlib.pyplot as plt  # 导入matplotlib库，用于绘图"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5afb78c-8d88-49a3-afa4-75db8f5bb14c",
   "metadata": {},
   "source": [
    "## 定义螺旋线的参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cdb932a5-d972-4e6d-a85e-184373e49ca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(0, 8 * np.pi, 200)  # 定义参数t，从0到8π，分200个点"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bb63878-5db9-4947-a00a-7d164f1cccc7",
   "metadata": {},
   "source": [
    "## 螺旋线的参数方程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "21b5794a-5dce-43d0-a657-2c99f021888f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.cos(t)  # 定义x1坐标，使用cos函数\n",
    "x2 = np.sin(t)  # 定义x2坐标，使用sin函数\n",
    "x3 = t  # 定义x3坐标，随t线性增加"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb4be0bf-e4eb-4066-a5bc-9f6a9a7c79ac",
   "metadata": {},
   "source": [
    "## 创建图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "767a435f-4c7b-4f2f-8025-7b91155c8d20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()  # 创建图形对象\n",
    "ax = plt.axes(projection='3d')  # 创建三维坐标轴对象\n",
    "ax.plot(x1, x2, x3)  # 绘制螺旋线\n",
    "\n",
    "## 设置投影和坐标轴范围\n",
    "ax.set_proj_type('ortho')  # 设置投影类型为正交投影\n",
    "ax.set_xlim(-1.5, 1.5)  # 设置x轴范围\n",
    "ax.set_ylim(-1.5, 1.5)  # 设置y轴范围\n",
    "ax.set_zlim(0, t.max())  # 设置z轴范围，最大值为t的最大值\n",
    "\n",
    "plt.tight_layout()  # 自动调整布局\n",
    "ax.set_xlabel(r'$\\it{x_1}$')  # 设置x轴标签\n",
    "ax.set_ylabel(r'$\\it{x_2}$')  # 设置y轴标签\n",
    "ax.set_zlabel(r'$\\it{x_3}$')  # 设置z轴标签\n",
    "\n",
    "## 设置视角和网格样式\n",
    "ax.view_init(azim=-135, elev=30)  # 设置视角，方位角为-135度，仰角为30度\n",
    "ax.xaxis._axinfo[\"grid\"].update({\"linewidth\":0.25, \"linestyle\" : \":\"})  # 设置x轴网格线样式\n",
    "ax.yaxis._axinfo[\"grid\"].update({\"linewidth\":0.25, \"linestyle\" : \":\"})  # 设置y轴网格线样式\n",
    "ax.zaxis._axinfo[\"grid\"].update({\"linewidth\":0.25, \"linestyle\" : \":\"})  # 设置z轴网格线样式"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
